Tentukan nilai x dari: 1. |4-5x|=6 2. |2+3x|=|-5| 3. 2|3x-8|=10 4. 2x+|3x-8|=-4 5. 5|2x-3|=2|3-5x| Materi tentang persamaan nilai x yang memenuhi persamaan

Bab Nilai Mutlak

1. |4 - 5x| = 6

4 - 5x = 6
4 - 6 = 5x
x = -2/5
atau
4 - 5x = -6
4 + 6 = 5x
x = 10/5 = 2

2. |2 + 3x| = |-5|
|2 + 3x| = 5

2 + 3x = 5
3x = 5 - 2
x = 3/3 = 1
atau
2 + 3x = -5
2 + 5 = -3x
x = -7/3

3. 2|3x - 8| = 10
|3x - 8| = 10/2
|3x - 8| = 5

3x - 8 = 5
3x = 5 + 8
x = 13/3
atau
3x - 8 = -5
3x = -5 + 8
3x = 3/3 = 1

4. 2x + |3x - 8| = -4
|3x - 8| = -4 - 2x

3x - 8 = -4 - 2x
3x + 2x = 8 - 4
5x = 4
x = 4/5
atau
3x - 8 = -(-4 - 2x)
3x - 8 = 4 + 2x
3x - 2x = 4 + 8
x = 12

5. 5|2x - 3| = 2|3 - 5x|
|10x - 15| = |6 - 10x|

10x - 15 = 6 - 10x
10x + 10x = 6 + 15
20x = 21
x = 21/20

Mapel : Matematika
Kelas : X SMA
Bab : Mutlak

Pembahasan :
|4 - 5x| = 6
(4 - 5x)² - 6² = 0
(10 - 5x)(-2 - 5x) = 0
x = 2
x = -2/5

Hp : {-2/5 , 2}

————————————————
|2 + 3x| = |-5|
|2 + 3x| = 5
(2 + 3x)² - 5² = 0
(7 + 3x)(-3 - 3x) = 0
x = -7/3
x = -1

Hp : {-7/3 , -1}

————————————————
2|3x - 8| = 10
|3x - 8| = 5
(3x - 8)² - 5² = 0
(3x - 3)(3x - 13) = 0
x = 13/3
x = 1

Hp : {1 , 13/3}

————————————————
2x + |3x - 8| = -4
|3x - 8| = -4 - 2x
(3x - 8)² - (-4 - 2x)² = 0
(x - 12)(5x - 4) = 0
x = 4/5
x = 12

Hp : {4/5 , 12}

————————————————
5|2x - 3| = 2|3 - 5x|
[5(2x - 3)]² = [2(3 - 5x)]²
(10x - 15)² - (6 - 10x)² = 0
(-9)(20x - 21) = 0
-180x + 189 = 0
180x = 189
x = 189/180

Hp : {189/180}